MIT LIBRARIES
3 9080 02617 9884
Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium IVIember Libraries
http://www.archive.org/details/realwagerigiditiOOblan
DEWEY
15
)5-
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
REAL
THE
WAGE RIGIDITIES
AND
NEW KEYNESIAN MODEL
Olivier
Blanchard
Jordi Gali
Working Paper 05-28
October 31, 2005
Room
E52-251
50 Memorial Drive
Cambridge,
This
MA 02142
paper can be downloaded without charge from the
Network Paper Collection at
Social Science Research
http://ssrn.com/abstract=842285
MASSACHUSETTS INSTITUTE
OF TECHNOLOGV
NOV
1
h 2005
LIBRARIES
Wage
Real
Rigidities
and the
New
Keynesian Model*
Olivier Blanchard^
October 2005
Jordi Gali^
(first draft:
April 2005)
Abstract
Most
central banks perceive a trade-off between stabilizing inflation
lizing
the gap between output and desired output. However, the standard
Keynesian framework implies no such
inflation
non
We
that this property of the
the divine coincidence,
call
trade-off. In that
stabi-
new
framework, stabilizing
equivalent to stabilizing the welfare-relevant output gap. In this pa-
we argue
per,
of
is
and
is
new Keynesian framework, which we
due to a special feature of the model: the absence
trivial real imperfections.
focus on one such real imperfection, namely, real
baseline
new Keynesian model
is
extended to allow
wage
for real
When
the
rigidities,
the
rigidities.
wage
divine coincidence disappears, and central banks indeed face a trade-off between
stabilizing inflation
and
stabilizing the welfare-relevant
that not only does the extended model have
tions,
but
it
more
output gap.
realistic
We show
normative implica-
also has appealing positive properties. In particular,
it
provides a
natural interpretation for the dynamic inflation-unemployment relation found
in the data.
JEL
Classification: E32,
Keywords:
oil
E50
price shocks, inflation targeting,
monetaiy
policy, inflation iner-
tia.
Prepared for the FRB/.]MCB conference on "Quantitative Evidence on Price DeterminaWashington, D.C., September 29-30, 2005. We have benefited from comments at var-
tion,''
and conferences, including CR.EI-UPF, Bank of England, MIT, LBS-MAPMU
NBER Summer Institute, and Federal Reserve Board. We thank in
particular Marios Angeletos, Jeff Fuhrer, Andy Levin, Greg Mankiw, and Michael Woodford,
as well as our discussants Bob Hall and Julio Rotemberg, for useful comments. We arc grateful
ious seminars
Conference, U. of Oslo,
to
Anton Nakov
MIT
*
and
for excellent
research assistance.
NBER
CREI, MIT, UPF,
CEPR
and
NBER
^
A
.
On
standard new Keynesian (NK) model has emerged.
consists of Calvo price and/or
wage
staggering.
posed of an Euler equation and a Taylor
foundations than
decessor,
it
its
rule.
On
the supply side,
demand
the
With more
explicit
side,
it
com-
it is
microeconomic
Keynesian ancestor, and more relevance than
its
RBC
pre-
has become the workhorse in discussions of fluctuations, policy, and
welfare.
A
framework
central, albeit controversial, block in this standard
New
Keynesian Phillips curve (NKPC), which,
in its
is
the so-called
simple form, has the
fol-
lowing representation:
=P
IT
where w
is
is
inflation,
the output gap.
y
is
The
(log)
Erri+l)
+
output, y*
effects of
K {y
-
is (log)
y*)
(1)
natural output, and (y
changes in factors such as the price of
—
y*)
oil
or
the level of technology appear through their effects on natural output y*
From a
welfare point of view, the
inflation
and
model implies that
it is
desirable to stabilize
to stabilize the output gap. Equation (1) implies that the
two
goals do not conflict: Stabilizing inflation also stabilizes the output gap. Thus,
for
example,
in
response to an increase in the price of
oil,
the best policy
to keep inflation constant; doing so implies that output remains equal to
natural
is
its
level.
This property, which we shall
call
the divine coincidence contrasts with a wide-
spread consensus on the undesirability of pohcies that seek to fully stabilize
inflation at all times
lies
the
and at any cost
in
terms of output. That consensus under-
medium-term orientation adopted by most
inflation targeting central
banks.
In this paper,
we show that
property of the standard
this divine coincidence
NK
is
tightly linked to a specific
model, namely the fact that the gap between the
natural level of output and the efficient (first-best) level of output
and invariant
welfare-relevant output gap
is
constant
to shocks. This feature implies that stabilizing the output gap
the gap between actual and natural output
equivalence
is
—
is
—
equivalent to stabilizing the
— the gap between actual and
the source of the divine coincidence:
The
1.
See, e.g., Goodfricnd and King (1997) for discussion of the case
with the new Keynesian model.
efficient
output. This
NKPC
implies that
for price stability
associated
stabilization of inflation
constancy of the
is
consistent with stabilization of the output gap.
gap between natural and
stabilization of the output
gap
is
efficient
The
output implies in turn that
equivalent to stabilization of the welfare-
relevant output gap.
The property
just described can in turn be traced to the absence of
reai imperfections in the standard
NK
has been pointed to by
many
a number of labor market facts
for
once the
NK
The reason
model
is
constant, and
is
The
rigidities.
existence of real
now
wage
authors as a feature needed to account
(see, for
We show that,
example, Hall [2005]).
extended in this way, the divine coincidence disappears.
that the gap between natural and efficient output
is
trivial
model. This leads us to introduce one
such real imperfection, namely real wage
rigidities
non
affected by shocks. Stabilizing inflation
is
is still
no longer
equivalent
to stabilizing the output gap, but no longer equivalent to stabilizing the welfare-
relevant output gap. Thus,
Stabilization of inflation
now
it is
and
no longer desirable from a welfare point of view.
stabilization of the welfare-relevant output
gap
present the monetary authority with a trade-off. In the face of an adverse
supply shocks, in particular, the monetary authority must decide whether to
accommodate a higher
level of inflation or, instead,
keep inflation constant but
allow for a larger decline in the welfare-relevant output gap.
While we focus on the implications of
as
an example of a more
real
wage
general proposition.
rigidities,
The optimal
we
see our results
design of macroeco-
nomic policy depends very much on the interaction between
real imperfections
NK
limited. In partic-
and shocks. In the standard
ular, the size of real distortions
to
model these interactions are
is
either constant or varies over time in response
exogenous shocks to the distorting variables themselves
(e.g.
tax rates). This
has strong implications for policy, one of them being the lack of a trade-off in
response to most shocks, including conventional supply shocks. In
reality, distor-
tions are likely to interact with shocks, leading to different policy prescriptions.
In our model, this interaction works through endogenous variations in
markups, resulting from the sluggish adjustment of
is
real wages.
wage
However, this
not the only possible mechanism: a similar interaction could work, for exam-
ple,
through the endogenous response of desired price markups to shocks, as
Rotemberg and Woodford
in
(1996). Understanding these interactions should be
high on macroeconomists' research agendas.^
2.
Sec Gal], Gcrtlcr, and Lopcz-Salido (2005)
for
some evidence suggesting
tlie
presence of
At the same time, we see the extension of the
wage
rigidities as
more than an example
cyclical fluctuations. In fact, as
list
We
itself.
of inflation inertia,
believe
discuss below, the introduction of real
namely,
)),
show that
and can account
real
wage
model
—which
beyond that inherited from the
wage
for the
NK
lack of inflation ineHia
its
define as the degree of inflation persistence
output gap {y — y*)
We
real
of real imperfections affecting
overcomes a well known empirical weakness of the standard
(as represented in equation (1
we
we
model to incorporate
of this general proposition.
that real wage rigidities are high on the
rigidities
NK
rigidities are
good empirical
a natural source
fit
of traditional
Phillips curve equations.
The
rest of the
paper
is
organized as follows. In Section
new Keynesian model, with staggered
tortions,
2
and use
we introduce
it
real
meaningful trade-off
1
we
lay out a baseline
and no labor market
price setting
to illustrate the shortcomings discussed above. In Section
wage
rigidities,
and show how
between stabilization of
their presence generates a
inflation
and the welfare-relevant
output gap. Section 3 looks at the implications of alternative stabilization
cies.
dis-
poli-
Section 4 looks at the costs of disinflation. Section 5 relates our results
to the literature. Section 6 derives
some empirical
relations
between
inflation,
unemployment and observable supply shocks implied by our framework, and
provides some evidence on
the data. Section 7 concludes.
The Standard New Keynesian Model
1
The
its ability to fit
baseline framework below
discuss "supply shocks"
supply
M. We
is
standard, with one exception: In order to
we introduce a non-produced
interpret shocks to
input, with exogenous
M as supply shocks. For simplicity, we leave
out technological shocks, but, in our model, they would have exactly the same
implications as supply shocks.
data,
is
We
when going
to the
— through changes
in the
difference, relevant
that our supply shocks are directly observable
price of the relevant inputs
Firms.
The only
—while technological shocks are not.
assume a continuum
of monopolistically competitive firms, each
producing a differentiated product and facing an isoelastic demand. The pro-
important cyclical variations
in the size of
aggregate distortions.
duction function for each firm
is
given by:
Y=
where
Y
output, and
is
M and
A''
M'^N^-"
are the quantities of the two inputs hired
we
the firm (in order to keep the notation simple
when not
subscripts
(2)
by
ignore firm-specific and time
strictly needed).
Letting lower case letters denote the natural logarithms of the original variables,
the real marginal cost
is
given by:
mc = w — mpn
= w - (y-n)where
w
is
Each good
log(l
-
q)
(3)
the (log) real wage, assumed to be taken as given by each firm.
is
non-storable and
is
sold to households,
who consume
it
in
the
same period. Hence, consumption of each good must equate output.
We assume a large number of identical households,
People.
preferences, constant discount factor
C/(C,7V)
/3,
and period
= log(C)-exp{0
with time separable
utility given
by
——
+
1
where
C
is
composite consumption (with
goods equal to
e). A'' is
employment, and ^
elasticity of substitution
is
between
a (possibly time- varying) prefer-
ence parameter.^
The implied marginal
rate of substitution (in logs)
mrs =
While our focus
3.
is
c
+ (j)n +
is
given by:
(4)
$,
on supply shocks, we introduce preference shocks
for
two reasons.
First,
our (simplifying) assumption of a closed economy with no capital accumulation implies that
first
in
best
employment
is
invariant to supply shocks (but not to preference shocks). Thus,
the absence of preference shocks, the employment gap would coincide with employment.
Such nonrobust property could be misleading, especially in empirical applications. Secondly,
and as discussed below, the implications for output of strict inflation targeting policies \'ary
considerably depending on whether preference or supply shocks are the relevent disturbance
at any point in time.
Efficient Allocation (First Best)
1.1
Let us start by assuming perfect competition in goods and labor markets. In
we
this case
have, from the firms' side:
w = mpn
=
(5)
-
{y
n)
+
\og{l
-
a)
and, from the consumer-workers' side:
w = mrs
=
y
+
<pn
+
^
(6)
where we have imposed the market clearing condition
c
=
Combining both
y.
expressions yields the following expression for the first-best level of employment
rii
(we use the subscript "1" to denote values of variables associated with the
first-best
—or
efficient
— allocation)
(l
Note that
first-best
+ ,^)ni-log(l-a)-^
(7)
employment does not depend on the endowment
of the
non-produced input (because of exact cancellation of income and substitution
effects
implied by log utility and Cobb-Douglas technology), but
related to the preference shifter
put, denoted by yi,
is
Given
^.
first-best
employment,
it is
inversely
first-best out-
given by
y\
=a
m + {1
—
a) Ui
(8)
which, as expected, depends on both shocks.
1.2
Flexible Price Equilibrium (Second Best)
We
maintain the assumption that prices and wages are
into account the
From the
log(e/(£ —
monopoly power
of firms in the
is
the
markup
but we take
goods market.
firms' side, optimal price setting implies
1))
flexible,
mc +
ji^
=
of price over cost, coming from the
0,
where
fi^
=
monopoly power
of firms. Hence, using (3)
w=
Henceforth,
we
y
—n+
log(l
—
a)
—
fJ'
(9)
use subscript "2" to refer to the second-best (or natural) levels
Combining
of a variable, corresponding to the equilibrium with flexible prices.
(6)
and
(9),
we can determine second-best employment n2
(1
+4>)n2
which, under our assumptions,
changes
in
is
=
log(l
y2
-a)-^JP-^
independent of m, but
the preference parameter
=a
£^.
:
(10)
may
Second-best output
m + {I - a)
Note an important implication of this baseline
is
vary as a result of
in
turn given by:
n2
NK
(11)
model: While both
first-
and
second-best output vary over time, the gap between the two remains constant
and given by
yr-y2 =
That property, which
nominal
rigidities
is
common
found
'^^^8
(12)
to the vast majority of optimizing
in the literature, will play
models with
an important role
in
what
follows.
1.3
Staggered Price Equilibrium
Assume now
that price decisions are staggered a la Calvo. As
is
well
known,
in
that case, in a neighborhood of the zero-inflation steady state, the behavior of
inflation
is
described by the diflFerence equation:
TT
where
mc + jjP
= P E-n{+l)+\{mc + ^^)
(13)
denotes the log-deviation of real marginal cost from
a zero inflation steady state, and A
=
9~^{l
-
9){\
-
(39),
its
value in
with 9 representing
the fraction of firms not adjusting their price in any given period.'*
See, e.g. Gali and Gertler (1999) for a derivation. .A.n identical ropre,scnta.tion obtains
under the assumption of quadratic costs of price adjustment, as in Rotcmbcrg (1982). In tlie
4.
Substituting
and using
(6) into (3)
and
(10)
mc + ^P=(^——-I
Combining the previous two equations
(11),
we
obtain:
(J/-J/2)
gives us the
new Keynesian Philhps curve
(NKPC):
= 0En{+l) +
TT
=
where k
Inflation
A(l
+
—
(p)/{l
depends on expected
its
shocks appear directly
in
on the natural
(7/
-
yo)
(14)
a).
distance of output from
effect
K
and the output gap, defined
inflation
natural
level.
Note that neither supply nor preference
equation (14).
level of output,
as the (log)
They appear
j/2,
indirectly through their
and thus through the output gap
{y-y2)Equation (14) implies that stabilizing
output gap {y —
Now
7/2)-
is
from (12) that
recall
that stabilizing the output gap
inflation
—
(2/
2/2)
is,
equivalent to stabilizing the
(j/i
—
(y
=
S-
This implies
in turn, equivalent to stabilizing
the welfare-relevant (log) distance between output and
"
1/2)
its first-best level, i.e.
Putting the two steps together implies that stabilizing inflation
yi)-
equivalent to stabilizing the welfare-relevant (log) distance of output from
best.
This
is
what we
(log) distance
between the
first-
is
a consequence of the constancy of
and the second-best
5,
the
levels of output. In par-
because an adverse supply shock does not alter
any incentives
first
referred to as the divine coincidence in the introduction.
Note that the divine coincidence
ticular,
is
S,
it
does not create
monetary authority to deviate from a policy of constant
for the
inflation.^
A
number
inflation
of recent papers have introduced a trade-off between stabilization of
and
stabilization of the distance
latter case coefficient A
is
related to the
between output and
its first-best level
magnitude of price adjustment
costs.
See Roberts
(1995).
As
may be
useful to restate the semantic conventions we use in the
output which would prevail in the absence of imperfections
as the "efficient" or "first-best" level of output. We refer to the level of output which would
prevail in the absence of nominal rigidities as the "natural" or "second-b<^t" level of output.
We refer to the log distance between the actual level of output and the second-best level of
output as the "output gap." We refer to the log distance between the actual level of output
and the first-best level of output as the "welfare-relevant output gap". Similar statements
apply to employment and employment gaps.
5.
paper.
this section ends,
We
it
refer to the level of
by assuming
(explicitly or implicitly)
gap between
first-
exogenous stochastic variations
and second-best output.^
We
take a different approach.
introducing an additional real imperfection in the model,
fluctuations in the gap in response to shocks.
approaches to
We
assume that
result of
cally,
real
Wage
get endogenous
defer a discussion of the two
Rigidities
wages respond sluggishly to labor market conditions, as a
some (unmodelled) imperfection
we assume the
partial
or friction in labor markets. Specifi-
adjustment model:
w = ^ w{—l) +
{1
where 7 can be interpreted as an index of
We
We
we
—
'y)
mrs
(15)
real rigidities.^
view equation (15) as an admittedly ad-hoc but parsimonious way of mod-
eling the slow
adjustment of wages to labor market conditions, as found
wage
variety of models of real
"right"
model
is.^
An
rigidities,
without taking a stand on what the
is
presented in Appendix
2.
The algebra
complex, but the basic conclusions are the same as those presented
below.
The important assumption underlying equation
(15)
is
7.
is
unaffected.
is
more
the text
in
that the slow
adjustment be the result of distortions rather than preferences, so the
equilibrium
in a
alternative formalization, explicitly derived from stag-
gering of real wage decisions,
6.
By
later.
Introducing Real
2
in S, the
first-best
^
See Woodford (2004, section 4.5) for a general discussion of that approach.
In principle one would want to guarantee vj > mrs at all times, to prevent workers from
working more than desired, given the wage (as would be the case for example in a model where
wages set in bargaining vary over time, but always remain above the workers' reservation
wage). This would be easily achieved by introducing a (sufficienth' large) positive steady state
wage markup, as in
w=
7'u;(
— 1)
-I-
(1
—
7)(/Li.,u
+ mrs]
without altering any of the conclusions below, though at the cost of burdening the notation.
Other authors have adopted a similar assumption in order to model real wage rigidities.
8.
Hence, Kai and Linzert (2005) propose an analogous partial adjustment model in the context
matching model in order to account for the response of unemployment and inflation to
of a
monetary policy shocks. Alternative, but related, formalizations of real wage rigidities can be
found in Felices (2005), in a model with variable effort and shirking, and Rabanal (2004), in
a model with rule-of-thumb wage setters. Other authors have adopted a similar assumption in
order to model real wage rigidities.
9.
Danthine and Kurrnan (200.5) develop a model in which a real wage rigidity of a very
Next we examine the implications of real wage
of
employment and
Once again we
inflation.
rigidities
find
it
on the equilibrium
level
useful to start by looking
at the flexible price case.
Flexible Price Equilibrium (Second Best)
2.1
Assume
of
that prices and wages are flexible, so
employment. Note that the
From
above, using
(4), (15),
from the wage setting
vj
=
=
As
before,
from the
first-best level
we
is
solve for the second-best level
the
same
as before.
and our assumptions on technology
(2),
we have,
side:
w{~l) +
'y
-y
(1
-
{1
-
+
<pn
+ ^)
-y)
{y
-y)
[a{m - n)
{1
+
= {y-n) + log(l -a)- iiP
= a{rn — n) + log(l — a) —
ij,^
w{-l) +
+
4>)n
-\-
(16)
^]
firms' side:
y
w = mpn —
fjP
Putting the two together and rearranging terms, we can solve
output
j/2
for
second-best
and
as a function of first-best output yi (which remains unchanged,
given by (7) and (8)) and the two exogenous driving forces:
[y2
-yi+5] =
where
Q-y
~
e., [yoi-l)
-ja/ija
+
(1
-
-
2;i(-l)
7)(1
+
+
4>))
<5]
G
+ 0.,(1 - a)[Am +
{1
+ 0)-i A^]
[0, 1].
Equation (17) points to the key implication of the introduction of
rigidities:
The gap between
the
first
(17)
and second-best
levels of
real
output
wage
is
no
longer constant, fluctuating instead in response to both preference and supply
shocks.
Note further that
0-,
is
increasing in 7, implying that the size and persistence
of deviations of the gap between second- and first-best output are increasing
similar form arises as a result of non-standard preferences, which
make
tlie
disutihty of effort
a function of some "norm" which depends on the level and the change in the real wage.
normative implications of such a model would be clearly different from ours.
The
10
the degree of real rigidities. Hence, for instance, the effects of an adverse
in
supply shock (an unexpected decrease
by more than
first-best
over time.
assumed
On
are to decrease second-best output
steady state level
its
7).
Only gradually
as the
6,
wage adjusts
the other hand, in response to a preference shock that lowers
output (an increase
in
second-best output
.^),
efficient level of
falls
by
wage from adjusting upward
real rigidities prevent the
support the lower
less,
since the
sufficiently to
employment and output.
Staggered Price Equilibrium
2.2
We
m)
output (the gap being increasing in
does the size of that gap return to
first-best
in
can now solve
for the behavior of inflation
staggering a la Calvo. Combining
(2), (3),
and
under the assumption of price
and rearranging terms we
(16),
obtain
{mc+fj.P)
= {mc + fiP){-l)+X2
(18)
where
X2
is
=
(1
- a)"M(l -
+
7)(1
-
0)(y
y2)
+ ia{Ay -
Ays)]
a linear combination of the current and lagged distance of output from second
best.
Combining
(18)
with (13)
TT
=
13
yields:
En{ + 1) +
-^
— jL
X2
(19)
1
This
is
the relation between inflation and the output gap implied by our model.
Notice that as in the baseline
exact relation
tion,
model,
it is still
expected
and the output gap (now, both
inflation,
is still
the distance of output from
implies a constant {y
—
its
second-best
level; In
because what matters
second-best
1(3.
More
level,
accurately,
but from
it
an
infla-
and change). So
equation (19), a constant
2/2)-'°
NKPC
model, the divine coincidence no
longer holds, since stabilizing the output gap (y
is
level
is
consistent with fully stabilizing the ouput gap,
But, in contrast with the baseline
This
the case that there
— although with shghtly more complex dynamics—between
fully stabilizing inflation
TV
NKPC
for welfare
is
.tt,
which
j/2)
is
no longer desirable.
the distance of output not from
its first-best level.
implies a constant
—
in
its
In contrast to the baseline model,
turn implies an asymptotically constant
11
the distance between the
constant, but
To
see
what
inflation
is
instead affected by the shocks, as
combine
this implies,
and the distance
=
TT
/?
and the second-best
first-
of
employment from
1
output
is
no longer
we have shown above.
(19) with (17) to obtain the relation
1
"fL
between
its first-best level:
^
—-—
xi - -—
—
—
Eni+l) +
levels of
[Am +
7L
{I
+
(p)-^A^
(20)
1
where now
=
X1
(1
-
q)
1[(1
-
7)(1
+
(P){y
-y^+6)+ 7a(Aj/ -
Ayi)]
involves a linear combination of the current and lagged welfare- relevant output
gapInflation
depends on expected
output from
inflation,
a distributed lag of the distance of
and a distributed lag
its first-best level,
erence shocks. In other words, there
of both supply
no longer an exact
is
relation,
and
pref-
however
complex, between inflation and the welfare-relevant output gap. Thus, there
no way to stabilize both
and monetary policy
To understand
in the presence of either
is
supply or preference shocks,
faces a clear trade-off.
the basic source of the trade-off,
economy's factor price
be the
frontier. Let v
it
is
useful to look at the
real price of the
non-produced
input. Then, given the Cobb-Douglas assumption:
mc =
{I
Thus any shock that induces an
—
V
+
const
increase in the real price of the non-produced
input (say, an increase in the price of
wages or an increase
w+a
a)
oil)
in real
marginal
cost.
policy accommodation, the
outcome
will
must lead
either to a decrease in real
Depending on the degree of monetary
be reflected in output or
inflation.
can be seen clearly by deriving the inflation equation, now expressed
of
TT
Av and
=
/3
=
terms
the distance of output from first-best (see appendix for derivation):
En{+1) +
where F
in
This
-z
^-^
——
1
^.
— 7)r g
— a{l
[(1
[0,' llJ
L
is
~
r)(l
+
0)(1
- a)-'
{y
-
yi
+ 5) + Ta
Av] (21)
a monotonic transformation of the index of real
12
wage
rigidities 7.
Consider
now any shock
that drives up the real price of the non produced input.
v}^ StabiUzing inflation requires a proportional decline
real
wage
first best.
rigidity, this
Stabilizing instead the distance of output from
higher inflation.
We
in
wage; given
output relative to
best will lead to
first
explore this trade-off further in the next section.
Policy Tradeoffs
3
To
illustrate the implications of the trade off faced
easiest to look at
is
a
in the real
can only be delivered by a decrease
two extreme
random walk process
for the
policies.
by the monetary authority,
non-labor input endowment, so that
Suppose that the central bank
tion.
That requires y
=
first
yi
—
stabilizes the welfare-relevant
best) at a
= and
Am = Sm is
For convenience, we assume ^
a white noise process. Note that, in this case, first-best employment
distance of output from
it
level consistent
6 at all times. It follows
is
constant.
output gap (the
with zero average
infla-
from (20) that;
-r^ Em
TT^p En{+1) -
Solving under rational expectations gives:
7r
=
7
TT
—
-1) 1
So, stabilizing the welfare- relevant output
fr„
-PT
gap implies some accommodation of
adverse shocks through inflation, followed by a slow
(if
7
high) return to
is
normal.
Suppose instead that the central bank
(1
11.
-
7)(1
Note that v
is
+
4)){y
-yi+5)+ ja{Ay
endogenou.'j in our framework,
a negative supply shock (a drop
disutility of labor (a drop in ^).
in
m)
tt
=
- 70(1 -
a)
stabilizes inflation, so
-
Aiji)
and so an increase
in
c
£'77(4-!).
e„
Then:
=
may come from
or a preference shock that brings
either
down the marginal
13
Or
equivalently:
(y
=
yi)
output relative to
To
- ©7)^ + ©7
-(1
first
2/i(-i)I
+
(i
- q)07^™
best.
bank attaches some weight
the extent that the central
both inflation and the gap from
in
-
[y(-i)
surprisingly, this policy replicates the second best, with large fluctuations
Not
in
-
first best,
between. The important point
some weight on
activity,
may
it
is
optimal policy will be somewhere
that, so long as the central
depends on the degree of real wage
on
A, the degree of
nominal
bank puts
have to accommodate adverse supply shocks
through potentially large and long lasting increases
also
to stabilization of
rigidity, 7.
rigidity,
and
How
in inflation.
large
How
long lasting
depends also on
a, the share of the
7,
but
non-produced
input in production.
To
get a sense of the order of
magnitude of the implied movements
and the welfare-relevant output gap, we compute the
with respect to
v,
which we can interpret as the
in inflation
elasticity of those variables
real price of
oil,
under the two
extreme policies just described (and given the assumption of a random walk
process for the
endowment m).
Hence, under the policy that fully stabilizes the gap relative to
first best,
we
have
diT
dfr
dmc
dv
dmc
dv
dmc/d£r
A
I
~ Pj
dv/dsr,
Aa7
(l-/?7)(a7+(l-a))
Letting
/?
Klenow
to 0.025.
—
1,
and assuming an average price duration of
(2003)),
As
we have A
a benchmark,
~
0.5.-'"
We
six
months
(Bils
and
set the share of oil in production, a,
we assume 7 =
0.9,
which implies a
half-life for
the
adjustment of the real wage adjustment of 6 quarters.
12.
Empirical estimates of A are often
much
smaller (See for example Gali and Gertler (1998)).
literally and use the implied value
For the purposes of the present exercise we take our model
of A,
14
Under these assumptions we obtain |^
~
Hence, stabilizing the welfare-
0.11.
relevant output gap in response to an adverse supply shock which raises the
price of
oil by, say,
10 percent, implies an (annualized) inflation slightly above 4
percent on impact. Note however that the expression for |^
Hence,
in 7.
if
we
short run inflation of
1^
=
0.012,
and
—
we have |^ = 0.05
the same oil price hike down to
set
7
inflation
is
0.8
is
highly non-linear
bringing the impact on
,
2 percent. If
contained below 0.5 percent.
7
=
0.5 then
^'^
Let us consider next the quantitative impact on the welfare-relevant output
gap of the second extreme policy analyzed above,
inflation. In that case,
d{y-yi)
d{y-yi)/d£m
dv
dv/de-m
(1
(1
-
-
a)Q.y
a)(l
'(l-7)(l
Under our baseline calibration (with 7
supply elasticity (0
=
1)
we have
g^^
the welfare-relevant output gap in the
to a 10 rise in the price of
by the
AR
one that fully stabilizes
i.e.
we have
oil,
=
0.9)
=
flrst
- a,)
+
</')
and assuming a unit Frisch labor
—0.11, thus implying a reduction in
quarter of
1.1
percent in response
with the persistence of that deviation (measured
parameter 9^) being relatively smaU:
0.10.
When we
set
obtain a 0.5 percent output gap loss on impact with persistence 0.05.
7
=
If
7
0.8
=
we
0.5,
the corresponding numbers are 0.1 percent and 0.01.
While these numbers are rough and purely
illustrative,
they suggest a far from
quantitatively trivial policy trade-off resulting from the presence of real wage
rigidities.
Real
4
The
Wage
Rigidities
analysis above has stressed the role of real
meaningful policy trade-off
13.
and the Cost of Disinflations
in
wage
rigidities in
generating a
response to shocks. Here we briefly discuss their
Notice that the expression we derive corresponds to the short run multipHer, and does
not take into account subsequent changes
rfv(-l-fc)/rfc^ = -«7'= for k = 1, 2, ...)
in v,
though the
latter are small
(more
especifically,
15
—
implications for the output cost of disinflations
As
is
well
known, the standard
however small, between
off,
NKPC
inflation
14
implies the presence of a long run trade-
and the output gap.^^ To
illustrate this
point, consider a sudden, permanent, unexpected reduction in inflation from,
say,
>
TT*
to zero.
From
(14)
follows that, in the standard
it
permanent decline
disinflation leads to a
dy{+k)
in
model, this
output and real wages given by^^
-i—^
=
NK
TT*
K
and
dw{+k) = -
(^—^]
(l
+
1
for
A;
=
0,1,2,...
In the standard
NK
model, the real
effects of disinflations
mentioned above
tend to be small, at least for plausible parameter values. Assuming for example
P=
0.99, e
=
<p=l anda =
0.75,
0.025,
we have dy = -0.05
and
tt*
du;
~
0.1
Hence, a permanent reduction in inflation of 5 percentage points lowers the
TT*.
level of
output at
declines
by
0.1
all
horizons by 0.25 percentage points, while the real wage
percentage points.
Consider next the case with real wage
steady state with inflation
tt*,
rigidities.
Starting from an identical
equations (13) and (18) imply that in the period
immediately after the (assumed to be successful) implementation of price
output and real wages are at their natural
bility,
when
real
levels.
However,
in
sta-
the period
disinflation takes place, things are different since, in order to decrease the
wage
engineer a
to the level consistent with price stability, the central
much
larger recession.
To be
specific, the decline in
bank needs
to
output required
to stabilize prices in the period of the implementation of price stability
is
given
by:
k(1-7)
14.
We
are grateful to
Greg Mankiw
for raising
the que.stion that stimulated the present
analysis.
15.
See King and
Wohnan
(1996) for a detailed discussion of the steady state in the standard
new Kcynesian model.
16.
Intuitively, the reduction in
output comes from the increase
in
average markups. Calvo
price-setting implies that the higher the inflation rate, the lower are average markups. Thus,
—
lower inflation leads to an increase in average markups equivalently a decrease in real wages
so a decrease in labor supply, and thus a decrease in output.
,
16
The output
loss
wage
of real
is
increasing, in a highly non-linear way, with 7, the index
rigidities.
Assuming
from any given
loss resulting
for
example 7
disinflation
is
=
0.9,
the short-run output
multiplied by a factor of 10. Under
the simple calibration proposed above, moving from 5 percent inflation to zero
inflation
now
implies a short run output loss of 2.5 percentage points, a
non
negligible value.
Alternative Approaches
5
We
are not the
There are
tion.
first
to confront the divine coincidence
at least
a resolu-
setting.
^^
Distortion Shocks
5.1
frequently used approach has been to simply append an exogenous distur-
NKPC,
bance to the
between
ida. Gall
Taken
call
it
and Gertler
is
a
fix,
As we have
is
to
example variations
comes from, and why
seen, conventional supply shocks
One needs
it
to
belongs to
do not appear as
NKPC.
of authors however have
approach
stabilization (for example, Clar-
not an acceptable solution:
this additional disturbance
disturbances in the baseline
A number
and output gap
(1999)).
at face value, this
the equation.
this
a "cost-push" shock, and thus create a trade-off
inflation stabilization
know where
for
to offer
two alternative approaches: distortion shocks and more
complex nominal wage and price
A
and
shown that a potential
justification for
assume the presence of exogenous "distortion shocks",
in tax changes, or
changes
in desired
markups by firms
for
(see
example Smets and Wouters (2003), Steinsson (2003), and Clarida, Gali and
Gertler (2001)). Such shocks do not affect the relation between inflation and the
second-best value; they do however
output gap, the distance of output from
its
affect the distance of second-best
—which
**
output
is
affected
by the shock
— and
the introduction, models of endogenous desired markups along the lines
Rotcmberg and Woodford (1996, 1998) would also eliminate the divine
coincidence, very much for the same reason our real wage rigidity assumption does. Rotemberg
and Woodford restricted their analysis to the real implications of endogenous markups, without
exploring their consequences for inflation and monetary policy in the presence of nominal
17.
As discussed
in
of those developed by
frictions.
17
first-best
output
—which,
by assumption,
is
not affected by the shock. Thus,
they create a trade-off between stabilization of inflation and stabilization of the
welfare-relevant output gap.
Such distortion shocks do probably
exist,
divine coincidence no longer holds. But
supply shocks, such as movements
the model extended
in this
way
and, with respect to these shocks, the
it still
holds with respect to standard
in the price of oil or
still
the face of increases in the price of
technology shocks. Thus
implies that keeping inflation constant in
the right policy
oil is
—a proposition which,
again, seems implausible.
Alternative Structures of
5.2
Wage and
Price Setting
Yet another approach aimed at removing the divine coincidence has been to ex-
wage and
plore the implications of alternative structures of
Henderson, and Levin (2000; EHL, henceforth)
if
in particular
both wage decisions and price decisions are staggered a
between price
inflation
price setting. Erceg,
la
and the output gap no longer holds
have shown that
Calvo, the relation
exactly, implying a
trade off between price inflation stabilization and output gap stabilization.
To
assesfe their
argument, consider the baseline model of Section
with staggered price and wage setting a
Given our assumptions, wage inflation
^
tt"'
=
PEtv'"{+1)
la Calvo, as in
is
1,
but now
EHL.
described by the difference equation:
- X^{w - mrs -
^"')
= pEn'"{+i)-\^{w-w2) + x^n + Yzr^] {y-y2)
where W2 and yo
are, respectively, the
natural levels of the real wage and out-
put (now defined as those that would obtain under both
wages), ^t^
is
is
a constant desired wage markup, and
A^, is
flexible prices
and
a coefficient which
a function of structural parameters, including the Calvo parameter indexing
the probability that any individual
wage
is
reset in a given period (see
EHL
for
details).
18
—
Price inflation,
now denoted by
is
,
given by:
= 0EnP{+l) + Xp(mc +
vrP
fiP)
am + an - log(l -
=
PEtvP{+1)
+
=
l3ETrP{+l)
+ Xp{w-W2) + XpY^iy-y2)
Note that neither wage nor
both
tt^
cases, inflation
\p{w -
+ ii^)
a)
depends only on the output gap. In
price inflation
depends on the output gap and the distance of the wage
from the natural wage. Thus, the divine coincidence does not apply, either with
respect to price inflation, or with respect to wage inflation.
Let us define however the composite inflation rate
It
follows
from the definition
TV
=
where now k
Given that,
output
is
7.;
,
f\,,
EHL
in the
'
\
tt
=
(Au,.7rP
+ Ap7r'")/(A„, + Ap).
that:
= PEn{+l) +
>i
{y
-
yo)
(22)
.
model, the distance between
first-
and second-best
given by
M(l-a) _,
1 +
(p
where
ji
^
fi^
+ ji^ we
,
can rewrite (22)
Tf
=
/3£'7r(+l)
Hence the divine coincidence emerges
ing the distance of output from
first
+
as:
K (y
again,
best
is
-
yi
+
though
5)
in
a different guise: Stabiliz-
equivalent to stabilizing a weighted
average of wage and price inflation.
What
are the policy implications of this weaker form of the divine coincidence?
As shown by EHL, the utihty-based
policies
is
and wage
loss function
needed to evaluate alternative
a weighted average of the squares of the output gap, price inflation
inflation. In this context strict price inflation targeting
is
generally
suboptimal, and often involves welfare losses that are several times larger than
other, better designed policies. Interestingly, while strict output gap stabiliza-
tion (and hence stabilization of the composite inflation index)
only for a specific parameter configuration,
EHL
is
conclude that
exactly optimal
it is
nearly op-
19
Woodford
timal for a large range of parameter values (see also
Hence, and
6).
for all practical purposes,
EHL
missing in the
Beyond
its
NK
standard
for the
behav-
which appear more consistent with the data than those of the
model. This
is
the topic of this section.
Inflation Inertia
6.1
Equation
(14) implies that inflation will not outlive
any variation
in the
delay.
This
is
j
'
no longer the case under our proposed modification of the
As equation
resulting
NK
(19) shows, in the presence of real wage rigidities (7
change in the output gap, even
inflation.
output
and with no
gap. Closing the latter will be sufficient to stabilize inflation fully
on
also
of Inflation
normative imphcations, our model has implications
ior of inflation
is
model.
The Behavior
6
(2003), Chapter
a meaningful policy tradeoff
The reason
from a change
is
in
if
simple:
>
model.
0)
any
purely transitory, will have persistent effects
Any change
in the workers' reservation
output (and thus a change in employment),
wage
will affect
the real wage (and hence real marginal cost) only gradually, with that effect
outliving the eventual return of output to
To
illustrate this point, consider the
a white noise process (so py
=
0).
Note how
or real
7
=
wage
rigidities
is
1
+
^
is
will
2.7^M~^-)
k=l
increasing in 7. For 7
—inflation
level.
Equation (19) implies that inflation
^3^.. + A
inflation inertia
natural
hmiting case where the output gap follows
follow:
TT
its
=
white noise, just
—that
like
is,
in the
absence
the output gap. For
close to one, inflation exhibits considerable inertia, despite the lack of serial
correlation in the output gap.^^
18.
The
result that, in the absence of real rigidities, the persistence of inflation
of the output gap
whom we
thank
increases with 7.
is
not a general proposition.
for correcting us
on
A
counterexample
this point.
What
is
is
given in
true in general
is
equal to that
Rotemberg
is
(200.5),
that persistence
20
The previous point can
be illustrated by using a representation of inflation
also
dynamics more closely linked to the empirical
Multiplying both sides of equation (19) by
literature.
terms,
we
found
inflation equations
(1
—
7I/)
in the
and rearranging
get:
+ -^£7r(+l) + -^X2 + C
'r=—+V7r(-l)
+ P7
+ P7
P7
1
where C
=
[(/?7)/(l
+
(^r
Pi)]
—
(23)
1
1
—
£^(71"!
is
1))
white noise and 12
is
defined as
above.
Note that
this equation takes a
used
ifications
in
many
form very similar to the hybrid
NKPC
spec-
empirical and policy analysis applications, and which
allow for both backward-looking and forward-looking inflation terms (with coefficients
whose sum
is
close to one, as
relative weight of lagged inflation
is
from
to 1/(1
-I-
/?),
which
expected inflation declines from
The previous
is
/3
the case here).^^ In our model, the
tightly linked to the degree of real
Thus, as 7 increases from
rigidities.
rises
is
to
the coefficient on past inflation
1,
slightly greater
to /?/(l
+ P),
than 1/2; the
which
work.
is
coefficient
slightly less
on
than 1/2.
discussion provides a potential explanation for the significance of
lagged inflation in estimates of hybrid versions of the
feel fully
wage
comfortable in relating equation (23) to
The reason
is
that (23)
is
[1999]).
NKPC.
Yet,
we do not
of the existing empirical
not directly estimable since the natural level of
output, and by implication the output gap,
by Gall and Gertler
much
We
is
not observable (a point stressed
view the ad-hoc measures of the output gaps
used in the literature (which approximate the natural levels by some smooth
function of time) with
some
suspicion.
Fortunately, our model implies a representation of the inflation equation that
can be taken to the data. Perhaps surprisingly, the representation turns out
to be fairly close to the traditional Phillips curve equation relating inflation
to lagged inflation, the
unemployment
rate,
estimated for example by Gordon (1997)
19.
See, e.g. Fuhrer
and Moore
and a supply shock indicator
among
(1997), or Orphanidcs
(as
others.)
and Williams (2005).
21
Inflation
6.2
and Unemployment
In order to derive the inflation-unemployment relation implied by our model
proceed
The
two
in
to explicitly introduce
first is
we
steps:
unemployment. To do
so, let
n^ be implicitly
defined by
Note that n^ measures the quantity of labor households would want to supply
given the current wage and marginal utility of income."'' Accordingly, define
the (involuntary) rate of unemployment, u, as the (log) deviation between the
desired supply of labor
and actual employment;
u
Clearly, in the absence of
employment
as the
households. For 7
wage
>
0,
is
wage
=
n-s
—n
rigidities (7
=
0) there
is
no involuntary un-
always equal to the marginal rate of substitution of
the previous definition and some algebraic manipulation
of (15) give:
(1-7)0
1
Hence, in our model with real wage
(below)
some constant
ward) adjustment of
rigidities,
a rate of unemployment above
(implicitly normalized to zero) induces a
real wages.
ployment rate deviates from
downward
(up-
This adjustment goes on as long as the unem-
zero,
with the size of the implied response being
inversely related to 7, our index of real rigidities, but positively related to
</),
the slope of the labor supply.
The second
step consists in rewriting the inflation equation (19) in terms of
unemployment, and of the
input.
Some manipulation
Inflation
ment
20.
be
is
rate,
price rather than the quantity of the
gives (the algebra
is
a function of past and expected future inflation, of the unemploy-
and
of the change in the real price of the non-produced input.
Note that the two conditioning variables y and n generally
a first-best cqnilibriiini, which explains why, in general, n,,
in
non-produced
given in the appendix):
differ
As
from what they would
7^ 711
22
in
is
equation (23)
earlier, the
white noise, orthogonal to
term C
all
is
proportional to (n
variables at
expected future inflation, this specification
specifications of the Phillips curve,
of
and
oil
hand
—
<
is
l.^"*^
Except
for the
1))
presence of
which typically include changes
in the price
unemployment on the
right
^^
Equation (24) can be estimated using instrumental variables. To do
annual U.S. data on inflation (measured by the percent change
deflator), the civilian
raw materials index
unemployment
GDP
(relative to the
deflator).
resulting estimated equation
is
Our instrument
The sample
period
so,
we use
GDP
the
in
and the percent change
rate,
of four lags of the previous three variables.
The
and so
indeed quite close to traditional
other supply side factors in addition to
side.
— E{w\ —
PPI
in the
set consists
1960-2004.
is
(standard errors in brackets, constant not
reported):
7r= 0.667r(-l)+ 0.42E7r(+l) (0.09)
which accords, at
coefficients
(0.06)
+
least qualitatively,
with
0.018
Av +
inflation equals
(24). In particular, all the
sum
of coefficients on lagged
one cannot be rejected at the 5 percent
When we
impose
this restriction the resulting
7r= 0.527r(-l)+ 0.48f;7r(+l) (0.05)
estimated
(0.05)
0.08 m
(0.05)
+
level
and expected
(though not by
estimated equation
0.014 Az;
is:
+C
(0.009)
which again matches well the theoretical specification, though the
on unemployment and raw materials prices are only significant
coefficients
at the 10 percent
The
coefficients
on past and expected future
of 0.92.
The other
structural coefficients are not identified and cannot be
level.
P
C
(0.001)
have the right sign and are statistically significant. Furthermore,
the theoretical restriction that the
much).
0.20 u
(0.08)
recovered (they would be
if
we estimated the
full
inflation
imply a value
model, something
for
we have not
done).
Note that, in contrast with the representation (23), the coefficients on lagged and expected
independent of tlie degree of real wage rigidities, as measured by 7. Instead, that
parameter has an influence on the size of the unemployment coefficient. Of course, in a full
fledged general equilibrium model it would have an influence on the path of unemployment
21.
inflation are
itself.
22.
See, for example,
Gordon
(1997), or Blanchard
and Katz (1909).
23
Alternative approaches
6.3
Here again, we are not the
flation inertia implied
first
to offer potential solutions to the lack of in-
by the standard
NK
model. Three sets of alternative
explanations, different from ours, can be found in the literature:"''
Lagged indexation. A
simple way of generating inflation inertia has been to
NKPC,
simply append a lagged inflation term to the
has been
a
fix,
known
as the hybrid
NKPC. Taken
thus giving rise to what
at face value, this
is
again just
not an acceptable solution. Christiano, Eichenbaum, and Evans (2005),
Smets and Wouters (2003), and Steinsson (2004), among
others, have
shown
however that such a formulation can be derived from automatic indexation of
prices to past inflation by the firms that are not re-optimizing prices in any given
period.
We
also see this as
an unconvincing
fix,
with
little
basis in fact:
none
of the existing micro-studies of price setting uncover any form of mechanical
indexation to past inflation; instead the prices of individual goods appear to
remain unchanged
Dhyne
for several
et al. [2005]).
months, even quarters
in
some cases
(see, e.g.
2''
Relative wage concerns. In a
well
known
paper, Fuhrer and
have argued that one gets inflation persistence
in a
Moore
model of wage staggering
one assumes that wage setters care about their real wage relative to the
of other workers over the period during which their
(1995)
real
own nominal wage
Holden and DriscoU (2003) have shown however that
is
if
wage
fixed.
inflation persistence in
the Fuhrer-Moore speciflcation comes in fact from the assumption that workers
care about the real wages of workers in the previous period. In this sense, the
results
from Fuhrer and Moore come from an assumption similar to ours, the
assumption that real wages
this period
depend, to some extent, on real wages
last period.
A
in showing how different types
dynamics of inflation. A non-exhaustive list includes
Trigari (2004). Walsh (2004), Rabanal (2004), Danthine and Kurmann (2004), Felices (200.5),
Kraus and Lubik (2005), among others. The analysis in those papers typically focuses on the
effects of labor market frictions (of different types) on the persistence of the inflation and
output responses to an exogenous monetary policy shock.
24. The version of the hybrid NKPC proposed by Galf and Gertler (1999) which assumes a
23.
fourth set of papers adopt an approach closer to ours
of labor
market imperfections
affect the
fraction of rule-of-thumb, backward-looking price setters overcomes that problem, since those
firms are assumed to adjust their prices only occasionally, as conventional Calvo firms.
24
Sticky information: Mankiw and Reis (2002) have proposed a model
in
which
firms adjust prices every period, according to a pre-specified plan, but revise
that plan infrequently. Accordingly, current inflation
the result of decisions
is
based on news about future demand and cost conditions obtained
A
periods, in addition to current news.
property
as one at
previous
consequence of that "distributed lag"
the emergence of inertia in inflation. Again,
is
in
we view
that explanation
odds with the micro evidence; Firms do not seem
to adjust their
prices continuously according to a pre-specified plan; instead they typically
keep prices unchanged for long periods of time. Furthermore, recent survey-
based evidence suggests that firms review their prices more often than they
change them, exactly the opposite to what
models
7
(see Fabiani et
al.
is
assumed by sticky information
(2004)).
Conclusions
The standard new Keynesian framework
trade-off
between
inflation
and output gap
mative implications that arise from
it.
We
stabilization
and the
In the present paper
that the introduction of real wage rigidities
shortcoming.
often criticized for
is
is
a natural
way
its
lack of a
radical nor-
we have argued
to
overcome that
have proposed a tractable modification of the new Keyne-
sian framework that incorporates these real
wage
rigidities
and generates more
reahstic policy trade-offs.
Our model can
also
account
flation that are often
particular,
for
some aspects
of the empirical behavior of in-
viewed as inconsistent with the standard
we show how
the presence of real
wage
rigidities
of inflation inertia, implying a degree of inflation persistence
herited from output gap fluctuations. In addition, our
NK
model. In
becomes a source
model
beyond that
in-
yields a simple
representation of inflation as a function of lagged and expected inflation, the
unemployment
rate
we estimate that
data pretty
and the change
in the price of
relation using annual postwar
well.
The
latter result
may
is
fications that other authors
have used
component
lies in
in the
data,
we
find that
When
it fits
the
not be very surprising given that the
not too different from some of the ad-hoc speci-
resulting empirical equation
key difference
US
non-produced inputs.
in the older Phillips
curve literature.
A
the relevance (confirmed empirically) of a forward-looking
determination of infiation, a feature emphasized by the more
25
recent literature. In a sense, our framework helps bridge the gap between the
old
and new
Phillips curve literatures in a
way
that
is
consistent with the micro-
evidence on price setting.
There are several avenues that we plan to pursue, building on the framework
developed in the present paper.
On
we want
the theoretical front,
for real
wage
rigidity,
and
to dig deeper
and explore microfoundations
their implications for optimal
monetary
policy.
Micro
foundations, based for example on shirking (Felices 2005), on rule-of-thumb
wage
setters
(Rabanal 2004), or on bargaining (Hall 2005)
substantial departures from the
NK
may
lead to
benchmark than we have allowed
more
for here.
The
formalization offered by Hall for example implies modifying not only the
real
wage
ecjuation,
but also the specification of labor demand: In his model,
the real wage rigidity affects only the rents going to workers and firms, and thus
only the rate of job creation.
On
the empirical front,
we plan
to estimate a
model of
joint
wage and
price
inflation dynamics that combines both nominal and real rigidities in wage setting.
We
also plan to
conduct a quantitative analysis of the optimal monetary
policy response to a change in the price of
oil
or other
raw materials,
tion of alternative assumptions about the degree of real
wage
as a func-
rigidities
and the
persistence of the shock.
More
generally,
we hope our paper
contributes to raise macroeconomists' aware-
ness of the likely interactions between aggregate shocks and distortions, and of
the implications of these interactions for optimal macroeconomic policy.
26
References
Blanchard, Olivier
ciling
J.,
and Lawrence
Katz (1999): "Wage Dynamics: Recon-
F.
Theory and Evidence," American Economic Review, 89
Christiano, Lawrence
J.,
(2), 69-74.
Martin Eichenbaum, and Charles L. Evans (2001):
"Nominal Rigidities and the Dynamic Effects of a Shock to Monetary
Policy,"
NBER WP#8403.
Christoffel, Kai,
ity
and Tobias Linzert
and Labor Market Frictions
for
(2005):
"The Role
Wage
of Real
Unemployment and
Inflation
Rigid-
Dynamics,"
mimeo.
Mark
Clarida, Richard, Jordi Gali, and
A New
etary Policy:
vol. 37,
"The Science of Mon-
Keynesian Perspective," Journal of Economic Literature,
1661-1707.
Clarida, Richard, Jordi Call, and
Policy in
Open
vs.
Economic Review,
Dhyne
Gertler (1999):
Individual
"Optimal Monetary
Gertler (2001):
An
Closed Economies:
vol. 91, no. 2,
et al. (2004):
Mark
Integrated Approach," American
248-252.
"Price Setting in the Euro Area:
Some
Stylized Facts from
Consumer Price Data," mimeo.
Erceg Christopher, Dale Henderson, and Andrew Levin, (2000), "Optimal Mon-
Wage and
etary Policy with Staggered
Price Contracts," Journal of Monetary
Economics, 46(2), 281-313.
Fabiani, Silvia et
New
Felices,
the
(2004):
"The Pricing Behavior
of Firms in the Euro Area:
Guillermo (2005): "Can Information-Consistent Wages Help Explain
Dynamics
Fuhrer, Jeffrey
terly
al.
Survey Evidence," mimeo.
of Real
Wages and
C, and George
R.
Inflation?"
Moore
mimeo.
(1995): "Inflation Persistence", Quar-
Journal of Economics, No. 440, February, pp 127-159.
Gall, Jordi
and Mark Gertler
(1999): "Inflation
Dynamics:
A
Structural Econo-
metric Analysis," Journal of Monetary Economics, vol. 44, no.
Gall, Jordi,
Mark
Gertler,
2,
195-222.
David Lopez-Salido (2005): "Markups, Gaps, and
the Welfare Costs of Economic Fluctuations," mimeo.
27
Goodfriend, Marvin, and Robert G. King (1997): "The
and the Role
thesis
of
Monetary
Policy,"
NBER
New
Neoclassical Syn-
Macroeconomics Annual 1997,
231-283.
Gordon, Robert
Economic
Hall,
J.
(1997):
"The Time Varying NAIRU and
Policy," Journal of
Economic Perspectives,
its
Implications for
vol. 11 (1), 11-32.
Robert (2005): "Employment Fluctuations with Equilibrium Wage Stick-
iness,"
American Economic Review
vol. 95, no. 1, 50-64.
Holden, Steinar and .John Driscoll (2003): "Inflation Persistence and Relative
Contracting," American Economic Review, vol 93
King, Robert G., and Alexander L.
St.
Wolman
(4),
(1996): "Inflation Targeting in a
Louis Model of the 21st Century," Federal Reserve
vol. 78, no. 3.
(NBER
Kraus, Michael,
ties in
the
New
WP
A
Bank
of
St.
Louis Review,
no. 5507).
Thomas Lubik
(2005):
"The
(Ir)relevance of Real
Wage
rigidi-
Keynesian Model with Search Frictions," mimeo.
Mankiw, N. Gregory and Ricardo Reis
Prices:
1369-1372.
Proposal to Replace the
Journal of Economics,
CXVII,
vol.
(2002): "Sticky Information vs. Sticky
New Keynesian
Philhps Curve," Quartely
issue 4, 1295-1328.
Orphanides, Athanasios, and John Williams (2005): "Imperfect Knowledge, Inflation
Expectations and Monetary Policy," in
ford, eds.
The
in B.
Bernanke and M. Wood-
Inflation Targeting Debate, University of Chicago Press.
Rabanal, Pau (2004): "Real
Wage
Rigidities,
Endogenous Persistence, and Op-
timal Monetary Policy," mimeo.
Roberts, John (1995):
"New Keynesian Economics and
Journal of Money, Credit and Banking,
vol. 27,
the Phillips Curve,"
975-984.
Rotemberg, Julio (1982): "Monopolistic Price Adjustment and Aggregate Output," Review of
Economic
Studies, vol. 49, 517-531.
Rotemberg, Julio and Michael Woodford (1996): "Imperfect Competition and
the Effects of Energy Price Increases on Economic Activity," Journal of Money,
Credit
and Banking,
vol. 28,
549-577.
Rotemberg, Julio (2005): "The Persistence of Inflation Versus that of Real Marginal Cost in the
New Keynesian
Model," unpublished manuscript.
28
Sbordone, Argia (2002): "Prices and Unit Labor Costs: Testing Models of Pricing Behavior," Journal of
Monetary Economics,
vol. 45, no. 2, 26.5-292.
Smets, Frank, and Raf Wouters (2003): "An Estimated Dynamic Stochastic
General Equilibrium Model of the Euro Area," Journal of the European Eco-
nomic Association,
vol
1,
no. 5, 1123-1175.
Steinsson, Jon (2003): "Optimal
Persistence," Journal of
Monetary Policy
Monetary Economics,
Trigari, Antonella (2005): "Equilibrium
Dynamics,"
in
an Economy with Inflation
vol. 50, no. 7.
Unemployment, Job
flows,
and
Inflation
ECB WP#304.
Walsh, Carl (2005): "Labor Market Search, Sticky Prices, and Interest Rate
Policies"
,
forthcoming
in
Review of Economic Dynamics.
Woodford, Michael (2003): Interest and Prices. Foundations of a Theory of
Monetary
Policy, Princeton LIniversity Press.
29
Appendix 1: Derivation of Alternative Representations of
flation Dynamics in the Presence of Real Wage Rigidities
Throughout
this
In-
appendix we assume the marginal cost and wage setting sched-
ules:
mc +
fi^
= w — mpn +
w = 7w( — 1) +
(1
jjJ'
— ^)mrs
as well as the inflation equation implied by Calvo staggered price setting:
=
TT
Representation #1:
in
/3£7r(+l)
+ A(mc + ^lP)
(25)
terms of the gap between actual and second-
best output.
Combining the wage schedule with
w=
7^i;(
— 1) +
(2)
and
(4)
— 7)(am +
(1
(1
— a + 0)n +
^)
which can be combined with the marginal cost schedule to yield
mc+yP =
Setting
7(mc(-l)+/iP) + (l-7)(^-log(l-Q))4-(l-7)(l+</>)n-7Q(Am-An)
mc = mc( — 1) = — /i^
=
(1
-
7)(^
-
log(l
(flexible price
-
a))
+
(1
-
assumption):
7)(1
+ 4>)n2 - 7Q(Am - An2)
which can be subtracted from the equation immediately above to
mc + n^ =
Finally,
7(7nc(-l)
+
/i^)
+
we combine the previous
(1
-
7)(1
+
</))(n
-
no)
yield:
+ 7a(An - An2)
difference equation for real marginal cost with
the Calvo equation (25) and rewrite in terms of output to obtain:
n
=
pETr{+l)
+
" 7)(1 + 0)(y r^T^[(l
~ 7L — a
1
J/2)
+ ia{^y -
Aj/2)]
II
30
or, equivalently,
^
1
where lo
=
+
i3^[(l
-
+
;7r(-l)
7/3
^-£7r(+l) +
—
^ X2 + Q
1+/37
l+dl
-
'
7)(1
+
'P){y
-
^2)
'
+ 7a(Ay -
Aj/2)]
and C
=
tI^Ctt
-
^(ttI-I)).
Representation #2: in terms of the gap between actual and first-best
output, and underlying exogenous shocks.
Combining the wage schedule with
w=
— 1) +
7tt;(
(1
(2)
and
(4)
— 7)(am +
—a+
(1
(f))n
+ ^)
which can be combined with the marginal cost schedule to yield
mc+iJ'
= 7(mc(-l)+^P) + (l-7)(^-log(l-Q)) + (l-7)(l+(?!>)n-7Q(Am-An)
Using the expression
for first-best
employment, we can rewrite the previous
difference equation in terms of the welfare relevant
employment gap and the
underlying shocks:
mc+^P = 7(mc(-l)+^P)+(l-7)(l+0)(n-ni+(5)+7Q(An-A7ii)-7Q[Am+(l+0)~-'A^]
Combined with
n
we
(25)
obtain:
= PEn{+l)+
^ {(l-7)(l+0)(n-ni+(5)+7a(An-Ani)-7Q[Am+(l+0)~^A^]}
1 — 7L
'
^
or, equivalently,
-
-
^
-^(-1)
1+7/3
'
'
+ -——(1 1 +P7
+
-^— £;7r(+l)
1
+
/37
q)-1[(1
+
-T~7r^°'^^'^
1 +P7
(1
-
7)(1
+
</')(y
+ ^)"'^0 +
-
yi
+
5)
+
7a(At/ - Ayi)]
C
31
Representation #3:
terms of the gap between actual and
in
first-best
output, and the real price of non-produced input.
Combining the wage schedule with
w=
Using the
+
-ywi-l)
fact that
m—n
=
(1
and
(2)
(4)
- 7)(a(m -
{w —
+
v)
n)
+
(1
log(Q:/l
—
a), as implied
+
(l))n
+
by cost mini-
mization:
w — jw{ — l) +
(1
— y){a{w —
v)
+ a log(Q:/l ~
+
a)
(I
+
+
(f>)n
^)
Rearranging terms;
w = r w{-l) +
where F
= ^_^Z_
wage
rigidities 7.
Note
also that
mc +
which
is
Thus we
fjP
-
(1
,
- a)~^
r)(l
S
is
[0, 1]
(q log(a/l
n)
= w
— a{w —
v)
=
—
a)
li;
- av + +{1 +
a)
+
<j))n
£)
(26)
a monotonic transformation of the index of real
= w — a{m —
(1
-
—
—
log(l
a)
— a log a —
+Q
i;
+
fi^
—
a)
+
fJ'
a) Iog(l
—
a)
+
(1
—
a) log(l
— aloga -
(1
—
/^^
(27)
a version of the factor price frontier (allowing for variable markups).
see that
an increase in the
real price of the
dependently of the source, in principle any shock
downward pressure on
real
endowment input
may
(in-
do), will create both
wages and upward pressure on marginal
costs and,
hence, inflation.
Combining
mc +
We
iiP
(26)
^r
and
(27)
(toc(-I)
we obtain
+ fi^) +
(1
(after
-
some
r)(l
+ (p)
algebra):
(n
-
rii
+
(5)
+ To Av
(28)
can now rewrite inflation as
TT
= p Eni + l) +
-
[(1
-
r)(l
+
(/))
(n
-^
m
+
S)
+ Ta
Av]
32
or, equivalently,
r
i
+
where T
—+ —
,
.^
'
'
r^
i+/3r
= ^^^^^
€
,
,^
'
'
+ 0),
A(l-r)(l
7r(-l) + -—---E7r(+l) + -p
/3r
(i
XTa
— Au+C
^ {y-yi+5) + i+/3r
()-
^^
^'
'^
/?r)(i-cv)
-
^
^
'
[0, 1]
Representation #4: in terms of the unemployment rate and the real
price of the non-produced input.
First
we
derive a simple relationship between marginal cost, the
rate (defined as above),
mc +
We
and the employment gap:
— w—
jdP
=
{y
=
4)
—
[y
n)
—
log(l
—
marginal cost
mc +
=r
/i^
+
a)
j^l^
+ 4>ns+0-{y~n)-~\og{l-a)+yP
[u-
+
Un)
(1
+
4>){n
use the previous expression to substitute for
for real
unemployment
(n.
ni
+
—
ni
(5)
+ 5)
in the expression
in (28):
(mc(-l)
After rearranging terms
+
ijJ')
we obtain
(1
-
+ M^ -
r) [mc
,
u]
+ Ta Au
the difference equation:
(l-7)(l-a)(/i
mc = mc{ — l)
,
+
u
{-
a Av
7
which
is
well defined only
if
7 >
(notice that as
Combining the previous equation with
1
1+P
/
,^
'
'
P
1+P
r.
,
..
'
'
(25),
we
7 approaches
obtain:
A(l-a)(l-7)(/)
7(1
so does u).
+ /3)
a\
,
l+P
33
Appendix
A
2:
Model with Staggered Real Wage Setting
Consider an economy with staggered wage setting and
period a fraction
their wage.
The
1
—7
of workers,
indexation. Each
full
drawn randomly from the population,
motion
log-linearized law of
aggregate real wage
for the
reset
is
thus
given by
=
wt
where wl denotes the newly
ywt-i
wage
set
the following wage setting rule (up to
+
{I
-
'y)wl
period
in
order,
first
maximization implies
Utility
t.
and ignoring a constant term):
00
=
w:
{1
~
p'y)Y,{p'y)' Et{m.rst+k\t}
fc=o
00
=
{1
=
P-J Et{wt_f_i}
-
M^rst+k -
p-f)Y2i(^^)''
+
1-/37
^
l
+
,
_
e„
eu4{w: - wt+k)}
+
^ {mrst
eu,0
Wt
where Tnrst+k\t denotes the marginal rate of substitution
set its
wage
in
period
for
a worker
who
last
t.'^^
Combining both equations we obtain
w=^
where
P)
* =
+A
Let
,^
t
'^^t^ntm^n
w{-l)
+ ^P Et{w{+1)} +Amrs
A=
and
,J}~iV,^!2''2„
I
thus implying that in the steady state
w=
wi
— W2 and mfs = mrsi —
w~
.
(29)
Notice that
!
,
=
$(!
+
mrs.
mrs2- Using the fact that
loi
=
mrsi we
can write
w = (^w{-l) + ^PEw(+l)+Aii^s +
25.
who
The second
last set its
<^z
(30)
equality uses the fact that the marginal rate of substitution for a worker
wage
in period
4,
denoted by
mrst-i-k\t< is related to its
average counterpart
according to
mrst+k\t
where e^
is
=
rnrst+k
the wage elasticity of labor
-
demand
em<p(ui,'+t
for
- Wi+k)
a particular worker, under the assumption
of imperfect substitutability between workers in production.
34
where
=
z
{1
+ P)wi -
wi{-l) - PEwi{ + l)
= Awi- 0EAwi{+l)
and where
= Ampni
Awi
=
a{Am. — Ani)
= a[Am -
+
4>)-^
A^\
a function of the exogenous shocks (and as a result so
is
Notice also that
y
{I
=
yi
—
y2
(7
>
= a$T
T=
0),
y and
mrs =
Using these results we can rewrite (30)
y
where
w = mpni — mpn2 = —j^
y{~l)
+ a/?$T Ey{ + 1) -
is z).
+ 3^)
(1
y
,
where
as:
(1
- a)$T
z
a+Mi-a+s) Thus, to the extent that real wage rigidities are present
we will have $ > and hence fluctuations in the gap between first and
-
second best output
in
response to shocks.
Next we derive the implied
inflation equation. Notice that real marginal cost
is
given by
mc = w —
= w
{y
—
n)
—
ct
-\
1
— a (y
log(l
—
777.)
—
—
a)
—
log(l
a)
In terms of deviations from the flexible price equilibrium
mc +
ji
—
(w — Wo)
-\
1
— a [y
—
we have:
yo)
Notice that we can also rewrite (29) in terms of deviations from the flexible
price equilibrium values:
w -W2 = ^
{w - u;t)(-1)
+
$/3
E{w -
u;':.)(+l)
+A
(1
+
—^)
1
— Q
[y
-
y-y)
35
Collecting results
mc +
we obtain
= ^ (mc +
11
/i)(-l)
+
$/? E{m.c
+
ij){+l)
+
f{y - yi)
where
=
f{y-y2)
[A(l
+ (0/l-a)) + (a/l-a)] (y-ys)
-^-^iy-y2)i-l)-^0-^Eiy-y2)i+l)
1 — a
1 — a
Combined with
TT
where u
=
= PEn{+l) +
= (3ETr{+l) +
A£;(l
- $L -
Notice that there
and
is
making
obtain:
XE{l-<PL-~p<!>L-'^)f{y-y2)
XE{1 -
/3'l>L-i)/(yi
$L - P^L-^)f{y ~
-
yi)
+u
ya)-
no trade-off between stabilization of the output gap y — y2
stabilization of inflation. However,
to shocks,
we
inflation equation (13)
it
when 7 >
,
u
will fluctuate in
response
impossible to stabilize both inflation and the welfare-
relevant ouput gap.
36
t+23^1
39
Date Due
Lib-26-67
MIT LIBRARIES
"I
II
I
I
3 9080 02617 9884
tA:i'iW'ii'',!Mimi!iiiniu
i!uiill,')/lIiiHM(l.'(ifffil;'
IKlimtW.UiWVi-.lth:'
iiiii'wiiiniifiiimiuiuiiir
;